where \(\lambda _2\)  is the second smallest eigenvalue of \(L_n\) , and \(\mathbf {v}_F = \mathbf {v}_2\)  is the corresponding eigenvector, i.e. the Fiedler vector [1]}. The algebraic connectivity \(\lambda _2\)  of \(G\)  can be mathematically expressed as
\(\lambda _2 & = & \mathbf {v}_F^T ~ L_n ~ \mathbf {v}_F ~.\) 
